An Analysis of Implied Volatility, Sensitivity and Calibration of the Kennedy Model

The Kennedy model provides a flexible and mathematically consistent framework for modeling the term structure of interest rates, leveraging Gaussian random fields to capture the dynamics of forward rates. Building upon our earlier work, where we developed both theoretical results — including novel proofs of the martingale property, connections between the Kennedy and HJM frameworks, and parameter estimation theory — and practical calibration methods, using maximum likelihood, Radon–Nikodym derivatives, and numerical optimization (stochastic gradient descent) on simulated and real par swap rate data, this study extends the analysis in several directions. We derive detailed formulas for the implied volatilities implied by the Kennedy model and investigate their asymptotic properties. A comprehensive sensitivity analysis is conducted to evaluate the impact of key parameters on derivative prices. We develop a Monte Carlo simulation scheme tailored to the conditional distribution of the Kennedy field, enabling efficient scenario generation consistent with observed initial forward curves. Furthermore, we present closed-form pricing formulas for various interest rate derivatives, including zero-coupon bonds, caplets, floorlets, swaplets, and the par swap rate, expressed explicitly in terms of the initial curve. Finally, we calibrate the Kennedy model to market-observed caplet prices. The findings provide valuable insights into the practical applicability and robustness of the Kennedy model in real-world financial markets.